On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification

TLDR

The study investigates how dispersed small solid particles modify decaying homogeneous turbulence using direct numerical simulation. In a gravitational environment, particles transfer momentum anisotropically to small‑scale motion, and pressure‑strain correlations redistribute this energy across directions at the same wave number. The simulations show that particles raise high‑wave‑number turbulence energy, viscous dissipation, and energy transfer rates, leading to an initial kinetic‑energy increase that later decays faster than in particle‑free turbulence, but the anisotropic energy input induces a reverse cascade that builds low‑wave‑number energy and reduces the decay rate compared to particle‑free or zero‑gravity flows.

Abstract

The modification of decaying homogeneous turbulence due to its interaction with dispersed small solid particles (d/η<1), at a volumetric loading ratio φv≤5×10−4, is studied using direct numerical simulation. The results show that the particles increase the fluid turbulence energy at high wave numbers. This increase of energy is accompanied by an increase of the viscous dissipation rate, and, hence, an increase in the rate of energy transfer T(k) from the large-scale motion. Thus, depending on the conditions at particle injection, the fluid turbulence kinetic energy may increase initially. But, in the absence of external sources (shear or buoyancy), the turbulence energy eventually decays faster than in the particle-free turbulence. In gravitational environment, particles transfer their momentum to the small-scale motion but in an anisotropic manner. The pressure-strain correlation acts to remove this anisotropy by transferring energy from the direction of gravity to the other two directions, but at the same wave number, i.e., to the small-scale motion in directions normal to gravity. This input of energy in the two directions with lowest energy content causes a reverse cascade. This reverse cascade tends to build up the energy level at lower wave numbers, thus reducing the decay rate of energy as compared to that of either the particle-free turbulence or the zero-gravity particle-laden flow.